# World Football Elo Ratings

The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.[2]

## Top 100 ranking

The following table shows the top 100 teams in the World Football Elo Ratings on 14 October 2016, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Rankings are shown as they were on 20 October 2016.[4]

 AFC CAF CONCACAF CONMEBOL OFC UEFA

## Highest average ratings since 1970

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 September 2016. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.

Rank Country Avg Elo
1 2015.0
2 [a] 1985.5
3 1929.5
4 1926.7
5 1923.0
6 1916.4
7 1908.7
8 1889.8
9 [b] 1851.7
10 [c] 1832.8
11 1824.9
12 [d] 1815.9
13 1800.6
14 1789.1
15 1788.0
16 1777.1
1777.1
Rank Country Avg Elo
18 1771.6
19 1769.9
20 1741.7
21 1728.7
22 1726.2
23 1725.0
24 1705.3
25 1700.7
27 1696.8
26 1695.8
28 1694.9
29 1688.7
30 1678.0
31 1677.3
32 1664.3
33 1661.3
34 1658.5
Rank Country Avg Elo
35 1658.0
36 1646.3
37 1645.5
38 1643.3
39 1643.2
40 1641.8
41 1635.0
42 1631.8
43 1612.1
44 1607.9
45 1606.2
46 1605.3
47 1598.6
48 1597.6
49 1597.5
50 1596.0
51 1592.5

## List of number one teams

The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:

## Ranking by days as leader

10,295 30 November 1872 11 June 1988
8,842 16 June 1929 Current
8,294 12 June 1958 7 July 2014
5,857 4 March 1876 11 March 1904
[e] 4,367 25 July 1966 28 May 2016
2,979 2 July 1912 27 August 1920
2,673 6 June 1934 15 August 2006
2,597 12 September 1984 10 July 2007
2,502 5 September 1920 11 October 2013
2,281 28 August 1920 8 July 1931
1,694 17 May 1953 11 June 1958
[f] 1,213 31 March 1963 24 June 1988
922 29 Aug 1920 3 July 2014
11 27 May 1934 6 June 1934
8 27 June 2004 7 June 2005

## Elo all-time records

### All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.

### All-time highest ranking

The following is a list of national football teams ranked by their highest Elo ranking ever reached. Note that for the highest ranking/rating of a national football team the Elo ratings website ignores the ranking/rating before 30 matches have been played.

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).

Rank 1920s 1930s 1940s [o] 1950s 1960s
1 1916

1976

2043

2036

1965

2 1876

1970

2008

2015

1939

3 1851

1897

1891

1996

1928

4 1831

1883

1880

1915

1927

5 1822

1869

1861

1874

1923

6 1817

1864

1849

1856

1888

7 1783

1843

1846

1852

1871

8 1781

1821

1839

1829

1852

9 1773

1816

1831

1828

1844

10 1753

1810

1814

1808

1840

11 1744

1769

1788

1803

1825

12 1720

1764

1782

1798

1802

13 1703

1691

1751

1796

1791

14 1695

1683

1741

1753

1779

15 1678

1677

1719

1728

1737

Rank 1970s 1980s 1990s 2000s 2010s [p]
1 2065

1977

2002

1998

2056

2 2043

1969

1995

1988

2047

3 1952

1951

1959

1970

2044

4 1930

1933

1936

1964

2002

5 1887

1897

1926

1958

1977

6 1882

1895

1909

1945

1919

7 1876

1890

1907 1921

1889

8 1869

1887

1906

1895

1883

9 1862

1853

1878

1890

1883

10 1853

1852

1868

1881

1868

11 1841

1827

1849 1843

1865

12 1836

1825

1842 1840

1860

13 1834

1825

1841

1823

1854

14 1815

1824

1831

1810

1836

15 1808

1789

1829

1807

1799

16 1794

1788

1825

1792

1795

17 1780

1787

1811

1790

1787

18 1774

1786

1786

1788

1772

19 1769

1780

1784

1777

1771

20 1762

1779

1784

1775

1768

## Highest rated matches

A list of the 16 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4243 2182 2061 1 : 0 aet 2014-07-13 World Cup F Rio de Janeiro
2202 2041 2 : 4 2014-09-03 Friendly Düsseldorf
3 4219 2104 2115 0 : 1 aet 2010-07-11 World Cup F Johannesburg
4 4201 2101 2100 1 : 7 2014-07-08 World Cup SF Belo Horizonte
5 4200 2008 2192 3 : 2 1954-07-04 World Cup F Bern
6 4195 2065 2130 3 : 0 2013-06-30 Confederations Cup F Rio de Janeiro
7 4161 2054 2107 2 : 1 2010-07-02 World Cup QF Port Elizabeth
8 4159 2073 2086 0 : 1 1973-06-16 Friendly Berlin
9 4153 2061 2093 0 : 0 2011-06-04 Friendly Goiânia
10 4149 2170 1979 4 : 2 1954-06-30 World Cup SF Lausanne
11 4148 2142 2006 4 : 2 1954-06-27 World Cup QF Bern
12 4136 2076 2060 0 : 0 2014-07-09 World Cup SF São Paulo
2089 2047 1 : 0 2010-07-07 World Cup SF Durban
14 4127 2055 2072 1 : 0 1982-03-21 Friendly Rio de Janeiro
15 4118 2084 2034 2 : 1 1974-07-07 World Cup F Munich
16 4114 2098 2016 0 : 0 2016-06-26 Copa América F East Rutherford

## Biggest upsets

A list of the matches with the biggest point exchange. Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[t]
The nations' points before the matches are given.

Rank Point
exchange
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 91 1636 1764 8 : 1 1924-05-29 Olympic Games Paris
2 88 1761 * 1902 7 : 1 1928-06-04 Olympic Games Amsterdam
3 84 1816 1963 6 : 1 1958-06-15 World Cup Helsingborg
4 83 * 1590 1823 3 : 0 1924-05-29 Olympic Games Paris
5 82 2101 2100 1 : 7 2014-07-08 World Cup Belo Horizonte
1190 1528 4 : 0 1980-02-23 OFC Nations Cup Nouméa
7 81 1599 1980 2 : 0 2006-06-17 World Cup Cologne
8 78 1875 2059 3 : 0 1998-07-04 World Cup Lyon
1229 1510 4 : 0 1972-05-14 Asian Cup Bangkok
1600 1974 3 : 0 1929-11-01 Copa América Buenos Aires
11 77 1786 2123 3 : 0 1959-12-12 Copa América Guayaquil
12 76 1965 2089 5 : 1 2014-06-13 World Cup Salvador
1866 1768 0 : 5 2009-07-26 CONCACAF Gold Cup East Rutherford
1553 1885 3 : 0 1937-01-10 Copa América Buenos Aires
15 75 1720 1995 5 : 3 1948-08-05 Olympic Games London
1684 * 1469 1 : 4 1946-03-10 CCCF Championship San José

*The national teams of Spain, Egypt and Guatemala had only played 27, 3, and 25 international matches before their respective upsets, and their Elo rating may still be partially determined by the starting rating they have been assigned (the points exchanges could be lower when these are adjusted).

## History

The Elo system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

## Overview

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

• The team's old rating
• The considered weight of the tournament
• The goal difference of the match
• The result of the match
• The expected result of the match

The different weights of competitions in descending order are:

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.

## Basic calculation principles

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings change are based on the following formulae:

${\displaystyle R_{n}=R_{o}+KG(W-W_{e})}$

or

${\displaystyle P=KG(W-W_{e})}$

Where;

 ${\displaystyle R_{n}}$ = The new team rating ${\displaystyle R_{o}}$ = The old team rating ${\displaystyle K}$ = Weight index regarding the tournament of the match ${\displaystyle G}$ = A number from the index of goal differences ${\displaystyle W}$ = The result of the match ${\displaystyle W_{e}}$ = The expected result ${\displaystyle P}$ = Points Change

The number of Points Change is rounded to the nearest integer before updating the team rating.

### Status of match

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup 60
Continental Championship and Intercontinental Tournaments 50
World Cup and Continental qualifiers and major tournaments 40
All other tournaments 30
Friendly Matches 20

### Number of goals

The number of goals is taken into account by use of a goal difference index.

If the game is a draw or is won by one goal

${\displaystyle G=1}$

If the game is won by two goals

${\displaystyle G={\frac {3}{2}}}$

If the game is won by three or more goals

• Where N is the goal difference
${\displaystyle G={\frac {11+N}{8}}}$

Table of examples:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

### Result of match

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

### Expected result of match

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

${\displaystyle W_{e}={\frac {1}{10^{-dr/400}+1}}}$

where dr equals the difference in ratings (add 100 points for the home team). So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

### Examples

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

#### Example 1

Team A versus Team B (Team A stronger than Team B)

 Score ${\displaystyle K}$ ${\displaystyle G}$ ${\displaystyle W}$ ${\displaystyle W_{e}}$ Total (P) Team A Team B Team A Team B Team A Team B 3 : 1 1 : 3 2 : 2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.679 0.321 0.679 0.321 0.679 0.321 +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

#### Example 2

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

 Score ${\displaystyle K}$ ${\displaystyle G}$ ${\displaystyle W}$ ${\displaystyle W_{e}}$ Total (P) Team B Team C Team B Team C Team B Team C 3 : 1 1 : 3 2 : 2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.529 0.471 0.529 0.471 0.529 0.471 +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

## Notes

1. ^ Representing West Germany from 1949 to 1990
2. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
3. ^ Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
4. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
5. ^ Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
6. ^ Combined record of the Russian Empire (1912-1914), RSFSR (1923), USSR (1924-1992), CIS (1992), and Russia (1992-present) national football teams.[8]
7. ^
8. ^
9. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
10. ^ as Zaire
11. ^
12. ^
13. ^ a b The combined Ireland national football team was in 4th to 6th place from its first match in 1882 to 1902, in a period that only 4 to 6 teams were in the rankings
14. ^ as Zaire
15. ^ In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
16. ^ up to 1 September 2016
17. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
18. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
19. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
20. ^ In those terms, most surprising may have been the 2:1 win of Luxembourg (Elo rating 1049) over Switzerland (ER 1730) in a World Cup qualification match in September 2008 (a 681 point difference). In another World Cup qualifier in October 2004 Liechtenstein (ER 1046) held the 810 points higher rated Portuguese team (ER 1856) to a 2:2 draw.

## References

1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
2. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
3. ^ World Football Elo Ratings Eloratings.net. Retrieved: 2016-10-14.
4. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 20 October 2016. Retrieved 2016-10-20.
5. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
6. ^ Arpad Elo, Chess Life, 1962.
7. ^ About the Chessmetrics Rating System, by Jeff Sonas
8. ^ "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04.